Question

a pharmacy technician receives a prescription for 500 ml of d12.5w. the pharmacy has d70 and sterile water for injection (swfi) in stock. how many ml of swfi does the technician need to prepare the solution?
108 ml
89 ml
392 ml
411 ml

question 33
1 point
a pharmacy technician receives a prescription for insulin with instructions to inject 45 units daily for 28 days. the pharmacy stocks 10-ml vials that have a concentration of 300 units/ml. how many vials should the technician plan to dispense?
three

Explanation:

First Question (D12.5W, D70, SWFI)

Step1: Define the dilution formula

We use the formula \( C_1V_1 = C_2V_2 \), where \( C_1 \) is the concentration of the stock solution (D70, which is 70% dextrose), \( V_1 \) is the volume of the stock solution, \( C_2 \) is the concentration of the desired solution (D12.5W, 12.5% dextrose), and \( V_2 \) is the volume of the desired solution (500 mL).

Step2: Solve for \( V_1 \)

Rearrange the formula to \( V_1=\frac{C_2V_2}{C_1} \). Substitute \( C_1 = 70\%, C_2 = 12.5\%, V_2 = 500\space mL \):
\( V_1=\frac{12.5\times500}{70} \)
\( V_1=\frac{6250}{70}\approx89.29\space mL \) (this is the volume of D70 needed)

Step3: Find volume of SWFI

The total volume of the desired solution is 500 mL. So the volume of SWFI is \( V_{SWFI}=V_2 - V_1 \)
\( V_{SWFI}=500 - 89.29\approx410.71\space mL\approx411\space mL \)

Second Question (Insulin Vials)

Step1: Calculate total units needed

Daily units: 45 units, days: 28. Total units \( = 45\times28 = 1260\space units \)

Step2: Calculate units per vial

Vial volume: 10 mL, concentration: 300 units/mL. Units per vial \( = 10\times300 = 3000\space units \)

Step3: Determine number of vials

Number of vials \(=\frac{1260}{3000}= 0.42\), but since we can't dispense a fraction of a vial, and we need to have enough, we round up? Wait, no—wait, 1 vial has 3000 units, which is more than 1260. Wait, maybe I made a mistake. Wait, 45 units daily for 28 days: 4528=1260 units. Each vial is 10 mL 300 units/mL = 3000 units. So 1 vial is enough? But the option is "Three"? Wait, maybe I misread. Wait, maybe the concentration is 300 units per mL? Wait, 10 mL vial with 300 units/mL: 10300=3000 units. 45 units per day for 28 days: 4528=1260 units. So 1 vial is enough. But the option is "Three"? Wait, maybe the question was miswritten, or I misread. Wait, maybe the concentration is 100 units/mL? No, the problem says 300 units/mL. Wait, maybe the daily dose is 45 units, but the insulin is U-100? No, the problem states 300 units/mL. Wait, perhaps the user's image has a typo, but assuming the calculation:

Wait, maybe I messed up. Let's recheck:

Total units: 45 * 28 = 1260 units.

Units per vial: 10 mL * 300 units/mL = 3000 units.

So number of vials: 1260 / 3000 = 0.42. Since we can't dispense 0.42 vials, we need 1 vial? But the option is "Three". Maybe the concentration is 100 units/mL? Let's check: 10 mL 100 units/mL = 1000 units. Then 1260 / 1000 = 1.26, so 2 vials? Still not three. Maybe the daily dose is 45 units, but the vial is 3 mL? No, the problem says 10 - mL vials. Alternatively, maybe the question is "45 units daily for 28 days" but the insulin is U-300 (300 units/mL). Wait, 45 units per day: volume per day is 45 / 300 = 0.15 mL per day. For 28 days: 0.15 28 = 4.2 mL. Each vial is 10 mL, so number of vials: 4.2 / 10 = 0.42, so 1 vial. But the option is "Three". Maybe there's a mistake in the problem, but based on the given numbers, 1 vial. However, if we assume that the concentration is 100 units/mL (common insulin concentration), then:

Total units: 45*28=1260.

Units per vial: 10*100=1000.

Number of vials: 1260/1000=1.26, so 2 vials. Still not three. Maybe the daily dose is 45 units, but the vial is 3 mL? No. Alternatively, maybe the question is "45 units three times daily"? Then total units: 45328=3780. Units per vial: 10300=3000. Then 3780/3000=1.26, so 2 vials. Still not three. Maybe the concentration is 100 units/mL, and daily dose 45 units three times: 45328=3780. Units per vial: 10100=1000. 3780/1000=3.78, so 4 vials. No. Alternatively, maybe the problem is "45 units daily for 28 days" with vial concentration 100 units/mL, vial volume 3 mL: 3*100=300 units per vial. 1260/300=4.2, so 5 vials. No. Maybe the original problem has a different number. But based on the given numbers, the first question's answer is 411 mL, and the second question—assuming the numbers are correct—1 vial, but the option is "Three", which suggests a possible typo. However, proceeding with the given numbers:

Answer:

(First Question):
411 mL